A New Approach to the Criteria-Weighted Fuzzy Soft Max-Min Decision-Making Method and Its Application to a Performance-Based Value Assignment Problem

Year 2020, Volume: 9 Issue: 1, 19 - 36, 30.05.2020

Serdar Enginoğlu , Samet Memiş

Abstract

Recently, the criteria-weighted fuzzy soft max-min decision-making (WFSMmDM) method provided in [Razak, S. A., Mohamad, D., A decision making method using fuzzy soft sets, Malaysian Journal of Fundamental and Applied Sciences, 2013, 9(2), 99-104] has been configured to operate in the fuzzy parameterized fuzzy soft matrices (fpfs-matrices) space by Enginoğlu and Memiş [A configuration of some soft decision-making algorithms via fpfs-matrices, Cumhuriyet Science Journal, 2018, 39(4), 871-881] faithfully to the original. Even though this configured method, which is denoted by RM13 and constructed by and-product/or-product (RM13a/RM13o), is useful in soft decision-making, it is of great importance to improve the method in terms of running time and complexity when processing a large number of data. In this study, to improve WFSMmDM, we propose two algorithms, denoted by EM20a and EM20o. Furthermore, we prove that EM20a is equivalent to RM13a. Thereafter, we compare the running time of these algorithms. The results show that EM20a and EM20o outperform RM13a and RM13o, respectively, in any number of data. We then apply EM20o to the problem of performance-based value assignment concerning seven filters used in image denoising. Besides, we compare the proposed two methods’ performance ranking with that of eight state-of-art soft decision-making methods. Finally, we provide the conclusive remarks and some suggestions for further research.

Keywords

Fuzzy sets, Soft sets, Soft decision-making, Soft Matrices, fpfs-matrices

Supporting Institution

Çanakkale Onsekiz Mart University

Project Number

FBA-2018-1367

Thanks

The authors thank Dr Uğur Erkan for technical support.

References

• Çağman, N., Enginoğlu, S. 2010a. Soft Set Theory and Uni-Int Decision Making. European Journal of Operational Research, 207(2): 848-855.
• Çaǧman, N., Enginoǧlu, S. 2010b. Soft Matrix Theory and Its Decision Making. Computer and Mathematics with Applications, 59(10): 3308-3314.
• Çağman, N., Enginoǧlu, S. 2012. Fuzzy Soft Matrix Theory and Its Application in Decision Making. Iranian Journal of Fuzzy Systems, 9(1): 109-119.
• Çağman, N., Çıtak, F., Enginoğlu, S. 2010. Fuzzy Parameterized Fuzzy Soft Set Theory and Its Applications. Turkish Journal of Fuzzy Systems, 1(1): 21-35.
• Çağman, N., Çıtak, F., Enginoğlu, S. 2011a. FP-soft Set Theory and Its Applications. Annals of Fuzzy Mathematics and Informatics, 2(2): 219-226.
• Çağman, N., Enginoğlu, S., Çıtak, F. 2011b. Fuzzy Soft Set Theory and Its Applications. Iranian Journal of Fuzzy Systems, 8(3): 137-147.
• Deli, İ., Çaǧman, N. 2015. Relations on FP-soft Sets Applied to Decision Making Problems. Journal of New Theory, 3: 98-107.
• Enginoǧlu, S., Soft matrices, 2012. PhD Dissertation, Tokat Gaziosmanpaşa University, Graduate School of Natural and Applied Sciences, p. 89, Tokat, Turkey (In Turkish).
• Enginoğlu, S., Çağman, N. (n.d.) Fuzzy Parameterized Fuzzy Soft Matrices and Their Application in Decision-Making. TWMS Journal of Applied and Engineering Mathematics, In Press.
• Enginoğlu, S., Memiş, S. 2018a. A Configuration of Some Soft Decision-Making Algorithms via fpfs-matrices. Cumhuriyet Science Journal, 39(4): 871-881.
• Enginoglu, S., Memiş, S. 2018b. Comment on “Fuzzy soft sets” [The Journal of Fuzzy Mathematics, 9(3), 2001, 589–602], International Journal of Latest Engineering Research and Applications, 3(9): 1-9.
• Enginoğlu, S., Memiş, S. 2018c. A Review on An Application of Fuzzy Soft Set in Multicriteria Decision Making Problem [P.K. Das, R. Borgohain, International Journal of Computer Applications 38 (12) (2012) 33-37]. Eds: Akgül, M., Yılmaz, İ., İpek, A. Proceeding of The International Conference on Mathematical Studies and Applications 2018, pp. 173-178, October 4-6, Karaman, Turkey.
• Enginoğlu, S., Çağman, N., Karataş, S., Aydın, T. 2015. On Soft Topology. El-Cezerî Journal of Science and Engineering, 2(3): 23-38.
• Enginoglu, S., Memiş, S., Arslan, B. 2018a. Comment (2) on Soft Set Theory and uni-int Decision Making [European Journal of Operational Research, (2010) 207, 848-855]. Journal of New Theory, 25: 85-102.
• Enginoglu, S., Memiş, S., Öngel, T. 2018b. Comment on Soft Set Theory and uni-int Decision Making [European Journal of Operational Research, (2010) 207, 848-855]. Journal of New Results in Science, 7(3): 28-43.
• Enginoğlu, S., Ay, M., Çağman, N. Tolun, V. 2019a. Classification of the Monolithic Columns Produced in Troad and Mysia Region Ancient Granite Quarries in Northwestern Anatolia via Soft Decision-Making. Bilge International Journal of Science and Technology Research, 3(Special Issue): 21-34.
• Enginoğlu, S., Erkan, U., Memiş, S. 2019b. Pixel Similarity-Based Adaptive Riesz Mean Filter for Salt-and-Pepper Noise Removal. Multimedia Tools and Applications, 78(24): 35401-35418.
• Enginoğlu, S., Memiş, S., Çağman, N. 2019c. A Generalisation of Fuzzy Soft Max-Min Decision-Making Method and Its Application to A Performance-Based Value Assignment in Image Denoising. El-Cezerî Journal of Science and Engineering, 6(3): 466-481.
• Enginoğlu, S., Memiş, S. Karaaslan, F. 2019d. A New Approach to Group Decision-Making Method Based on TOPSIS under Fuzzy Soft Environment. Journal of New Results in Science, 8(2): 42-52.
• Maji, P. K., Biswas, R., Roy, A. R. 2001. Fuzzy Soft Sets. The Journal of Fuzzy Mathematics, 9(3): 589-602.
• Maji, P. K., Biswas, R., Roy, A. R. 2003. Soft Set Theory. Computers and Mathematics with Applications, 45(4-5): 555-562.
• Memiş, S. Enginoğlu, S. 2019. An Application of Fuzzy Parameterized Fuzzy Soft Matrices in Data Classification. Eds: Kılıç, M., Özkan, K., Karaboyacı, M., Taşdelen, K., Kandemir, H., Beram, A. Proceedings of International Conferences on Science and Technology Natural Science and Technology, pp. 68-77, August 26-30, Prizren, Kosovo.
• Memiş, S., Enginoğlu, S. Erkan, U. 2019. A Data Classification Method in Machine Learning Based on Normalised Hamming Pseudo-Similarity of Fuzzy Parameterized Fuzzy Soft Matrices. Bilge International Journal of Science and Technology Research, 3(Special Issue): 1-8.
• Molodtsov, D. 1999. Soft Set Theory-First Results. Computers and Mathematics with Applications, 37(4-5): 19-31.
• Razak, S. A., Mohamad, D. 2011. A Soft Set Based Group Decision Making Method with Criteria Weight. International Scholarly and Scientific Research & Innovation, 5(10): 1641-1646.
• Razak, S. A., Mohamad, D., A. 2013. Decision Making Method using Fuzzy Soft Sets. Malaysian Journal of Fundamental and Applied Sciences, 9(2): 99-104.
• Riaz, M., Hashmi, R. 2017. Fuzzy Parameterized Fuzzy Soft Topology with Applications. Annals of Fuzzy Mathematics and Informatics, 2017, 13(5): 593-613.
• Riaz, M., Hashmi, R. 2018. Fuzzy Parameterized Fuzzy Soft Compact Spaces with Decision-Making, Punjab University Journal of Mathematics, 50(2): 131-145.
• Riaz, M., Hashmi, R., Farooq, A. 2018. Fuzzy Parameterized Fuzzy Soft Metric Spaces. Journal of Mathematical Analysis, 9(2): 25-36.
• Sezgin, A., Çağman, N., Çıtak, F. 2019. α-Inclusions Applied to Group Theory via Soft Set and Logic. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1): 334-352.
• Şenel, G. 2018. Analyzing The Locus of Soft Spheres: Illustrative Cases and Drawings. European Journal of Pure and Applied Mathematics, 11(4): 946-957.
• Ullah, A., Karaaslan, F., Ahmad, I. 2018. Soft Uni-Abel-Grassmann’s Groups. European Journal of Pure and Applied Mathematics, 11(2): 517-536.
• Zorlutuna, İ., Atmaca, S. 2016. Fuzzy Parametrized Fuzzy Soft Topology. New Trends in Mathematical Sciences, 4(1): 142-152.